W. Buchmüller

CP violation and R invariance in supersymmetric models of strong and electroweak interactions

Abstract We investigate the general structure of the minimal supersymmetric extension of the standard model of strong and electroweak interactions. Certain terms in the effective lagrangian, which may yield too large a neutron electric dipole moment, are not allowed by R invariance. The hypothesis of a partially conserved R current suppresses also the transition μ→eγ as well as dimension-5, B - and L -nonconserving operators. Furthermore, it has interesting implications for the strong CP problem.

Quarks and leptons as quasi Nambu-Goldstone Fermions

Abstract We discuss a new idea for constructing composite quarks and leptons which have (approximately) vanishing mass. They are associated with fermionic partners of Goldstone bosons arising from the spontaneous breakdown of an internal symmetry G f in a supersymmetric preon theory. For G f = SU(5) being broken to SU(3) × U(1) em there arise as quasi Goldstone fermions, naturally and unequivocally, precisely the quarks and leptons of one family. The dynamics of these quasi Goldstone fermions is explored by constructing a general supersymmetric nonlinear effective lagrangian. By means of a reduced model, we show that the first nontrivial interactions of the quasi Goldstone fermions can give rise, in an effective way, to the weak interactions. Issues connected with the incorporation of families in the scheme and the generation of masses, as well as the possible structure of the underlying preon theory are briefly discussed.

Quasi nambu-goldstone fermions

The Fermi-Bose symmetry, namely supersymmetry is presumably the only way of combining internal symmetries with Lorentz invariance in our 4 dimensional space-time, and is also expected to be useful for understanding the existence of massless fermions in terms of a well-defined geometry.1) Although there has not been observed any experimental evidence on such a symmetry yet, our feeling is that the super-Poincare algebra is so elegant and beautiful that it must be relevant at some underlying level.

Fine- and hyperfine structure of quarkonia

It is pointed out that the flux tube picture of electric confinement, which led to the “Coulomb plus linear” potential model, also predicts the structure of spin-dependent forces in heavy quark systems for large and small distances. The corresponding hamiltonian is obtained from a semiclassical argument and applied to the fine structure of the ψ and ϒ families.

Weak interactions of quasi nambu-goldstone fermions

Abstract We investigate the hypothesis that the observed weak interactions are the residual interactions of quasi Goldstone fermions. Left-handed quarks and leptons arise from the spontaneous symmetry breaking U(6) → U(4) × SU(2) in a supersymmetric theory. The simplest preon model realizing this breakdown leads, in the complementary picture, to the supersymmetric extension of the standard model of electroweak interactions. Furthermore, t Hoofts anomaly conditions are satisfied with respect to the unbroken subgroup of the U(6) flavour symmetry and R -invariance. The preon model predicts the existence of a ninth chiral supermultiplet, the novino.

Chiral symmetry and supersymmetry in the Nambu-Jona-Lasinio model

Abstract The connection between chiral symmetry and supersymmetry is investigated in the context of a supersymmetric extension of the Nambu-Jona-Lasinio model. A supersymmetric gap equation is found and it is shown that no solution exists which breaks chiral symmetry. A simple physical argument for this phenomenon is given and possible implications for the dynamics of composite models are discussed.

Zero mass states in QCD2

Abstract We study, for N arbitrary, SU( N ) QCD in two dimensions, in the massless quark limit. We show that this theory possesses an exact zero mass bosonic bound state, which persists if the quarks are put in the adjoint representation or if the confining group is changed to SU( N )×SU( M ). If an additional local U(1) interaction is added this state acquires a mass g 1 2 / π , as expected from anomaly considerations. The massless bosonic state saturates the chiral anomaly, implying that no zero mass fermionic bound states are in the theory. The relevance of our results for composite models of quarks and leptons is discussed.

Composite Higgs fields from a σ-model for leptons

Abstract We study a supersymmetric σ-model which contains the leptons of one family and an additional singlet as Goldstone superfields. Supersymmetry is softly broken through a scalar mass Δ. Quantum effects generate two composite chiral superfields with the quantum numbers of two Higgs doublets. Their vacuum expectation values break the local SU(2)W×U(1)y symmetry to U(1)EM. The mass spectrum of the theory is calculated as a function of Δ and the σ-model scale f.

The Structure of Weak Interactions for Composite Quarks and Leptons

Abstract We consider a model of quarks and leptons as quasi-Goldstone fermions which is based on an underlying supersymmetric SU(2)HC × SU(2)′HC preon theory. The spontaneous breakdown of a global U(6) × U(6)′ × U(1) symmetry to U(4) × U(4)′ × SU(2)diag creates both quarks and leptons and at the same time allows for the possibility of having either residual or fundamental weak interactions. Effective lagrangians in the confining phase of the theory are compared to those emerging from a complementary picture and the problems connected with the nature of the weak interactions are discussed in this context also.

Supersymmetric bound states

Abstract We investigate the bound-state spectrum of a supersymmetric version of QED and calculate the energy of the lowest states of the theory to O(α4). These states involve a degenerate quartet of spin - 1 2 and spin-zero states (para-states) and a degenerate quartet of spin - 1 2 states associated with an additional spin zero and spin one state (ortho-states). Because of the supersymmetry, the ortho-para splitting in positronium is changed from 7 12 mα 4 to 1 2 mα 4 .